## virtus 3 years ago Find the volume of the solid formed when the area bound by the curve y=4-x^2 and the x axis is rotated one complete revolution about the y axis

1. sauravshakya

first find the critical points and use integration

2. amistre64

or just consider one side of it

3. virtus

can you just tell me the answer , because i am getting the wrong answer. I got 16 pi units but the answer is 8 pi units and i don't know where i went wrong.

4. virtus

*units ^3

5. amistre64

6. amistre64

|dw:1342094312271:dw| this can be done by shells or disks; which way are you most comfortable with?

7. amistre64

i think i know why youre twice as big as the answer; your prolly integrating the whole thing across

8. amistre64

your in effect sweeping the same volume twice when you do that

9. sauravshakya

10. amistre64

|dw:1342094460320:dw| if we do shells:$\int_{0}^{2}2pix(4-x^2)dx$ $2pi\int_{0}^{2}x(4-x^2)dx$ $2pi\int_{0}^{2}4x-x^3\ dx$ $2pi\left(\frac{1}{2}4x^2-\frac{1}{4}x^4\right)_{0}^{2}$

11. virtus

oh i think i understand. I apologise amistre64 if i sounded rude before. I had no intentions whatsoever to offend you.

12. amistre64

no offense taken :)

13. virtus

@amistre64 i thought it was around y axis, shouldn't be dy not dx ?

14. amistre64

depends on your method; i used the shell method, which opens up along the x axis the disc method would travel along the y

15. amistre64

teh disc method we would have to convert y=x into its inverse x=y, which isnt that hard to do, but just takes extra steps :)

16. virtus

oh i see, so for the shell method where does the x come from in x(4-x^2)

17. amistre64

think of the shell method as finding the area of a sheet of paper, or a flattened out tin can. the width of the paper is the circumference of the base circle|dw:1342095061762:dw| the height of the paper is the function that it hits along the way. Area = base (2pi x) * height (f(x))

18. amistre64

|dw:1342095194082:dw|

19. virtus

OH I GET IT NOW ! thanks @amistre64

20. amistre64

youre welcome